Look-Up Table (Simulink Reference)

Simulink Reference

Look-Up Table

Approximate a one-dimensional function using the specified lookup method

Library

Simulink Look-Up Tables and Fixed-Point Blockset LookUp

Description

The Look-Up Table block computes an approximation to some function y=f(x) given data vectors x and y.

Note To map two inputs to an output, use the Look-Up Table (2-D) block.

The length of the x and y data vectors provided to this block must match. Also, the x data vector must be strictly monotonically increasing after conversion to the input's fixed-point data type, except in the following case. If the input x and the output signal are both either single or double, and if the lookup method is Interpolation-Extrapolation, then x may be monotonically increasing rather than strictly monotonically increasing. Note that due to quantization, the x data vector may be strictly monotonic in doubles format, but not so after conversion to a fixed-point data type.

You define the table by specifying the Vector of input values parameter as a 1-by-n vector and the Vector of output values parameter as a 1-by-n vector. The block generates output based on the input values using one of these methods selected from the Look-up method parameter list:

Interpolation-Extrapolation--This is the default method; it performs linear interpolation and extrapolation of the inputs.

If a value matches the block's input, the output is the corresponding element in the output vector.
If no value matches the block's input, then the block performs linear interpolation between the two appropriate elements of the table to determine an output value. If the block input is less than the first or greater than the last input vector element, then the block extrapolates using the first two or last two points.

Interpolation-Use End Values--This method performs linear interpolation as described above but does not extrapolate outside the end points of the input vector. Instead, the end-point values are used.
Use Input Nearest--This method does not interpolate or extrapolate. Instead, the element in x nearest the current input is found. The corresponding element in y is then used as the output.
Use Input Below--This method does not interpolate or extrapolate. Instead, the element in x nearest and below the current input is found. The corresponding element in y is then used as the output. If there is no element in x below the current input, then the nearest element is found.
Use Input Above--This method does not interpolate or extrapolate. Instead, the element in x nearest and above the current input is found. The corresponding element in y is then used as the output. If there is no element in x above the current input, then the nearest element is found.

To create a table with step transitions, repeat an input value with different output values. For example, these input and output parameter values create the input/output relationship described by the plot that follows:

Vector of input values:   [-2 -1 -1  0 0 0 1 1 2]
Vector of output values:  [-1 -1 -2 -2 1 2 2 1 1]

This example has three step discontinuities: at u = -1, 0, and +1.

When there are two points at a given input value, the block generates output according to these rules:

When the input signal u is less than zero, the output is the value connected with the point first encountered when moving away from the origin in a negative direction. In this example, when u is -1, y is -2, marked with a solid circle.
When u is greater than zero, the output is the value connected with the point first encountered when moving away from the origin in a positive direction. In this example, when u is 1, y is 2, marked with a solid circle.
When u is at the origin and there are two output values specified for zero input, the actual output is their average. In this example, if there were no point at u = 0 and y = 1, the output would be 0, the average of the two points at u = 0. If there are three points at zero, the block generates the output associated with the middle point. In this example, the output at the origin is 1.

The Look-Up Table block icon displays a graph of the input vector versus the output vector. When a parameter is changed on the block's dialog box, the graph is automatically redrawn when you click the Apply or Close button.

When the Show additional parameters check box is selected, some of the parameters that become visible are common to many blocks. For a detailed description of these parameters, refer to Block Parameters in the Fixed-Point Blockset documentation.

To avoid parameter saturation errors, the automatic scaling script autofixexp employs a special rule for the Look-Up Table block. autofixexp modifies the scaling by using the output look-up values in addition to the logged minimum and maximum simulation values. This prevents the data from being saturated to different values. The look-up values are given by the Vector of output values parameter (the YDataPoints variable).

Parameters and Dialog Box

Vector of input values: Specify the vector of input values. The input values vector must be the same size as the output values vector. Also, the input values vector must be strictly monotonically increasing after conversion to the input's fixed-point data type, except in the following case. If the input values vector and the output signal are both either single or double, and if the lookup method is Interpolation-Extrapolation, then the input values vector may be monotonically increasing rather than strictly monotonically increasing. Note that due to quantization, the input values vector may be strictly monotonic in doubles format, but not so after conversion to a fixed-point data type.
Vector of output values: Specify the vector of output values. The output values vector must be the same size as the input values vector.
Show additional parameters: If selected, additional parameters specific to implementation of the block become visible as shown.

Look-up method: Specify the lookup method. See Description for a discussion of the options for this parameter.
Output data type mode: You can set the output signal to a built-in data type from this drop-down list, or you can choose the output data type and scaling to be the same as the input. Alternatively, you can choose to inherit the output data type and scaling by backpropagation. Lastly, if you choose Specify via dialog, the Output data type, Output scaling value, and Lock output scaling against changes by the autoscaling tool parameters become visible.
Output data type: Specify any data type, including fixed-point data types. This parameter is only visible if Specify via dialog is selected for the Output data type mode parameter.
Output scaling value: Set the output scaling using radix point-only or [Slope Bias] scaling. This parameter is only visible if Specify via dialog is selected for the Output data type mode parameter.
Lock output scaling against changes by the autoscaling tool: If selected, scaling of outputs is locked. This parameter is only visible if Specify via dialog is selected for the Output data type mode parameter.
Round integer calculations toward: Select the rounding mode for the fixed-point output.
Saturate on integer overflow: If selected, overflows saturate.

Conversions and Operations

The Vector of input values parameter is converted from doubles to the input data type. The Vector of output values parameter is converted from doubles to the output data type. Both conversion are performed offline using round-to-nearest and saturation. Refer to Parameter Conversions in the Fixed-Point Blockset documentation for more information about parameter conversions.

Examples

Suppose the Look-Up Table block in the above model is configured to use a vector of input values given by [-5:5], and a vector of output values given by sinh([-5:5]). The following results are generated.

Look-Up Method
Input
Output
Comment

Interpolation-Extrapolation
1.4
2.153
N/A

5.2
83.59
N/A

Interpolation-Use End Values
1.4
2.153
N/A

5.2
74.2
The value for sinh(5.0) was used.

Use Input Above
1.4
3.627
The value for sinh(2.0) was used.

5.2
74.2
The value for sinh(5.0) was used.

Use Input Below
1.4
1.175
The value for sinh(1.0) was used.

-5.2
-74.2
The value for sinh(-5.0) was used.

Use Input Nearest
1.4
1.175
The value for sinh(1.0) was used.

Look-Up Method	Input	Output	Comment
`Interpolation-Extrapolation`	`1.4`	`2.153`	N/A
`5.2`	`83.59`	N/A
`Interpolation-Use End Values`	`1.4`	`2.153`	N/A
`5.2`	`74.2`	The value for `sinh(5.0)` was used.
`Use Input Above`	`1.4`	`3.627`	The value for `sinh(2.0)` was used.
`5.2`	`74.2`	The value for `sinh(5.0)` was used.
`Use Input Below`	`1.4`	`1.175`	The value for `sinh(1.0)` was used.
`-5.2`	`-74.2`	The value for `sinh(-5.0)` was used.
`Use Input Nearest`	`1.4`	`1.175`	The value for `sinh(1.0)` was used.

Characteristics

Dimensionalized
Yes

Direct Feedthrough
Yes

Sample Time
Inherited from driving block

Scalar Expansion
No

Zero Crossing
No

Dimensionalized	Yes
Direct Feedthrough	Yes
Sample Time	Inherited from driving block
Scalar Expansion	No
Zero Crossing	No

Logical Operator Look-Up Table (2-D)